Browser CSS is always version behind

Can't figure out why this is happening, but my browser is always displays previous version of BrowserSync's CSS, but HTML updates properly with new CSS file. Doesn't seem to be related to specific browser. I think I've had the same issue with Gulp before I've started using .stream() in BS, but I'm not sure if it can be used with Webpack.

const {
  themename,
  serverUrl,
  pathtothemefolder
} = require('./theme-constants');

const globImporter = require('node-sass-glob-importer');
const MiniCssExtractPlugin = require('mini-css-extract-plugin');
const BrowserSyncPlugin = require('browser-sync-webpack-plugin');
const FixStyleOnlyEntriesPlugin = require('webpack-fix-style-only-entries');
const ImageminPlugin = require('imagemin-webpack-plugin').default;
const imageminGuetzli = require('imagemin-guetzli');
const CopyWebpackPlugin = require('copy-webpack-plugin');

var path = require('path');

module.exports = {
  entry: './main.js',
  output: {
    path: path.resolve(__dirname, './'),
    filename: 'bundle.js',
    publicPath: './' + themename
  },
  module: {
    rules: [
      /*      {
              test: \/js-src/!*.js$/,
              exclude: /node_modules/,
              use: {
                loader: 'babel-loader',
                options: {
                  presets: [
                    [
                      '@babel/preset-env',
                      {
                        'useBuiltIns': 'entry'
                      }
                    ]
                  ]
                }
              }
            },*/
      {
        test: /\.(png|jpg|gif|svg|webp)$/,
        exclude: /node_modules/,
        loader: 'url-loader',
        options: {
          name: '[name].[ext]?[hash]',
          limit: 8192,
          publicPath: '../images/',
        }
      },
      {
        test: /\.(scss|sass)$/,
        exclude: /node_modules/,
        use: [
          {
            loader: MiniCssExtractPlugin.loader
          },
          // {
          //   loader: 'style-loader' // creates style nodes from JS strings
          // },
          {
            loader: 'css-loader',
            options: {
              sourceMap: true
            }
          },
          {
            loader: 'postcss-loader',
            options: {
              sourceMap: true
            }
            // }, {
            //   loader: 'resolve-url-loader',
            //   options: {
            //     sourceMap: true
            //   }
          },
          {
            loader: 'sass-loader',
            options: {
              importer: globImporter(),
              sourceMap: true,
            }
          }
        ]
      }
    ]
  },
  devtool: 'source-map',
  plugins: [
    // Copy the images folder and optimize all the images
    new CopyWebpackPlugin([{
      from: 'img-src/images',
      to: themename + '/images'
    }]),
    new ImageminPlugin({
      test: /\.(jpe?g|png|gif|svg)$/i,
      cacheFolder: './cache',
      svgo: {
        removeTitle: true
      },
      plugins: [
        imageminGuetzli({
          quality: 85
        })
      ]
    }),
    new FixStyleOnlyEntriesPlugin(),
    new MiniCssExtractPlugin({
      // Options similar to the same options in webpackOptions.output
      // both options are optional
      filename: themename + '/css/style.css',
      chunkFilename: themename + '/css/[id].css'
    }),
    new BrowserSyncPlugin({
        proxy: {
          target: serverUrl,
          ws: true
        },
        serveStatic: [{
          route: pathtothemefolder,
          dir: './' + themename
        }],
        files: [
          themename + '/css/*',
          themename + '/templates/*',
          themename + '/blueprints/*',
        ],
        injectCss: true,
        open: false,
        cors: true
      },
      { reload: false }
    )
  ],
};

Tried adding ReloadDelay in case it served the CSS file too soon, but it's not the case.

Va1 / browser-sync-webpack-plugin

Browser CSS is always version behind #75